Question
Find six rational numbers between $3$ and $4.$
✓
Answer
Given that to find out six rational numbers between $3$ and $4$
We have, $3\times\frac{7}{7}=\frac{21}{7}$ and $4\times\frac{6}{6}=\frac{28}{7}$
We know $21 < 22 < 23 < 24 < 25 < 26 < 27 < 28 $
$\frac{21}{7}<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<\frac{28}{7}$
$3<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<4$
Therefore, $6$ rational numbers between $3$ and $4$ are $\frac{22}{7},\frac{23}{7},\frac{24}{7},\frac{25}{7},\frac{26}{7},\frac{27}{7}$ Similarly to find $5$ rational numbers between $3$ and $4$, multiply $3$ and $4$ respectively
with $\frac{6}{6}$ and in order to find $8$ rational numbers between $3$ and $4$ multiply $3$ and $4$ respectively
with $\frac{8}{8}$ and so on.
We have, $3\times\frac{7}{7}=\frac{21}{7}$ and $4\times\frac{6}{6}=\frac{28}{7}$
We know $21 < 22 < 23 < 24 < 25 < 26 < 27 < 28 $
$\frac{21}{7}<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<\frac{28}{7}$
$3<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<4$
Therefore, $6$ rational numbers between $3$ and $4$ are $\frac{22}{7},\frac{23}{7},\frac{24}{7},\frac{25}{7},\frac{26}{7},\frac{27}{7}$ Similarly to find $5$ rational numbers between $3$ and $4$, multiply $3$ and $4$ respectively
with $\frac{6}{6}$ and in order to find $8$ rational numbers between $3$ and $4$ multiply $3$ and $4$ respectively
with $\frac{8}{8}$ and so on.
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